This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A033582 #33 Dec 02 2024 12:22:18
%S A033582 0,7,28,63,112,175,252,343,448,567,700,847,1008,1183,1372,1575,1792,
%T A033582 2023,2268,2527,2800,3087,3388,3703,4032,4375,4732,5103,5488,5887,
%U A033582 6300,6727,7168,7623,8092,8575,9072,9583,10108,10647,11200,11767,12348,12943,13552,14175
%N A033582 a(n) = 7*n^2.
%C A033582 From _Roberto E. Martinez II_, Jan 07 2002: (Start)
%C A033582 Number of edges of the complete bipartite graph of order 8n, K_n,7n.
%C A033582 Number of edges of the complete tripartite graph of order 5n, K_n,n,3n. (End)
%H A033582 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A033582 Central terms of the triangle in A132111: a(n) = A132111(2*n,n). - _Reinhard Zumkeller_, Aug 10 2007
%F A033582 a(n) = 7*A000290(n). - _Omar E. Pol_, Dec 11 2008
%F A033582 a(n) = 14*n + a(n-1) - 7 (with a(0) = 0). - _Vincenzo Librandi_, Aug 05 2010
%F A033582 G.f.: -7*x*(1+x)/(x-1)^3. - _R. J. Mathar_, Feb 06 2017
%F A033582 From _Amiram Eldar_, Feb 03 2021: (Start)
%F A033582 Sum_{n>=1} 1/a(n) = Pi^2/42.
%F A033582 Sum_{n>=1} (-1)^(n+1)/a(n) = Pi^2/84.
%F A033582 Product_{n>=1} (1 + 1/a(n)) = sqrt(7)*sinh(Pi/sqrt(7))/Pi.
%F A033582 Product_{n>=1} (1 - 1/a(n)) = sqrt(7)*sin(Pi/sqrt(7))/Pi. (End)
%F A033582 From _Elmo R. Oliveira_, Dec 02 2024: (Start)
%F A033582 E.g.f.: 7*exp(x)*x*(1 + x).
%F A033582 a(n) = n*A008589(n) = A195041(2*n).
%F A033582 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2. (End)
%t A033582 7Range[0, 49]^2 (* _Alonso del Arte_, Jun 30 2013 *)
%o A033582 (PARI) a(n)=7*n^2 \\ _Charles R Greathouse IV_, Jun 17 2017
%Y A033582 Cf. A000290, A008589, A132111, A195041.
%K A033582 nonn,easy
%O A033582 0,2
%A A033582 _N. J. A. Sloane_